Enzyme Kinetics and Metabolic Control Analysis
225
R,
=
rJk,
,v’+6 1
+
and
R-
,
=
rJk-,
v + c
We now expand R, and R2 from the point
P =(x°,s’= l,y° = s,°/s°)
„0
, 5Ä,
dR,
,
dRt ,
,
Do
dRt
,
dR Jdy
,
dv
,
,
Ä, =Ä, H
------ tir
h
-------t/y + —
- ds = R
. + — Lc£c + — L —
dx + — ds
H
------ -tfc'
dx
dy
ds'
dx
dy {dx
ds'
J
ds’
(4)
(5)
(
6
)
R2
=R°2
+ ^ d y =
dR*
dy
dy
l^dx
ds'
(7)
At P the dimensionless rates are:
r : = t
l-x°
~^-=R°2
0 \ \
L
1
+ b\
1 + 7
v° +
c
= J ’(x \s°)
/ 7
(
8
)
As point
P
we choose x° = 0.5, while
is chosen such that
a
,
b
and
c
have the values given to them in
Fig. 6.8, i.e.
a
= 1 and
b= c =
0.5. Using (3) (or (6.28)) and (4)
y° =
0.22474
and
=
R°2
= J°
= 0.3101
(
The partial derivatives evaluated at
P
are:
2
=
dx
lac
a I
a
....
...
- - -
a + -
b
b\
v
b
V
b
(
10
)
2
dy
ds’
a
a
a
---------x° | +
b
b
b
a + --------
x
b
b
lac
_
n
a
a
2 v° + a + - - -
x
b
b
(11)
previous page 248 Bioreaction Engineering Principles, Second Edition  read online next page 250 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off